Generalized Browder's and Weyl's Theorems for Generalized Derivations
arXiv:1306.0499
Abstract
Given Banach spaces $\X$ and $\Y$ and Banach space operators $A\in L(\X)$ and $B\in L(\Y)$, let $ρ\colon L(\Y,\X)\to L(\Y,\X)$ denote the generalized derivation defined by and , i.e., ($U\in L(\Y,\X)$). The main objective of this article is to study Weyl and Browder type theorems for $ρ\in L(L(\Y,\X))$. To this end, however, first the isolated points of the spectrum and the Drazin spectrum of $ρ\in L(L(\Y,\X))$ need to be characterized. In addition, it will be also proved that if and are polaroid (respectively isoloid), then is polaroid (respectively isoloid).
13 pages; research article